It has been proved that \(F_z(r_{ij \cdot \mathcal {K}})\)  quickly approaches a Gaussian distribution \(\mathcal {N}\)  \((\frac{1}{2}\ln {\frac{1+\rho _{ij \cdot \mathcal {K}}}{1-\rho _{ij \cdot \mathcal {K}}}}, \frac{1}{N-|\mathcal {K}|-3})\)  for any \(\rho _{ij \cdot \mathcal {K}}\)  as the sample size \(N\)  approaches infinity [1]}. Therefore, we set the null hypothesis as \(H_0(i, j \vert \mathcal {K}): \rho _{ij \cdot \mathcal {K}} = \rho _0 = 0\)  and the alternative hypothesis as \(H_1(i, j \vert \mathcal {K}): \rho _{ij \cdot \mathcal {K}} = \rho _1 \ne 0\) , and \(H_0\)  is rejected with significant level \(\alpha \)  if \(|F_z(r_{ij \cdot \mathcal {K}})| > \frac{\Phi ^{-1}(1-\alpha /2)}{\sqrt{N-|\mathcal {K}| - 3}}\) , where \(\Phi \)  is the cumulative distribution function of a standard normal distribution [2]}.
